From Hard Drop - Tetris Wiki

Nintendo Wi-Fi Connection , also known as Nintendo WFC for short, was a service run by Nintendo that allowed free online play all over the world. It was used by Nintendo DS and Wii games. It was succeeded by Nintendo Network.
This service ended for DS and Wii games on May 20, 2014.

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Tetris DS Nintendo Wifi Connection

This is primarily a technical document describing the servers that the Nintendo DS connected to (before it was discontinued) to perform Nintendo Wifi. It would appear that at login, Tetris DS reported what it believed to be its rank to Nintendo. This also occured every time you switched opponents. This process was done via a handshake between the DS and Gamespy. This is also what allowed the device known as action replay to be so nasty to the highscore board.

Sidenote: Many of the IP's listed below are also used by the Wii gaming system (not just the DS).